Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #9100 |
498 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(62,65,67,78)(63,69,71,76)(64,73,75,89)(66,80,81,77)(68,82,83,92)(70,85,79,84)(72,86,87,93)(74,90,91,88);(54,56,57,61,58,55,59,60)(62,64,66,74,67,75,81,91)(63,68,70,72,71,83,79,87)(65,73,80,90,78,89,77,88)(69,82,85,86,76,92,84,93);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55,57,60,58,56,59,61)(62,63)(64,72)(65,76,78,69)(66,79)(67,71)(68,74)(70,81)(73,86,89,93)(75,87)(77,84,80,85)(82,88,92,90)(83,91)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=g,d^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^52,e^b=eg,d^c=dg,f^c=fg1826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 65068);